The degree measure of `(7pi)/6` is

Options

A. `160^(@)`
B. `210^(@)`
C. `250^(@)`
D. `270^(@)`

Answer

To convert the radian measure of \( \frac{7\pi}{6} \) to degrees, we can follow these steps:

### Step 1: Understand the relationship between radians and degrees.
We know that:
\[ 2\pi \text{ radians} = 360 \text{ degrees} \]
This means that \( 1 \text{ radian} = \frac{360}{2\pi} \text{ degrees} \).

### Step 2: Set up the conversion formula.
To convert radians to degrees, we can use the formula:
\[ \text{Degrees} = \text{Radians} \times \frac{360}{2\pi} \]

### Step 3: Substitute the given radian measure into the formula.
Now, we will substitute \( \frac{7\pi}{6} \) into the formula:
\[ \text{Degrees} = \frac{7\pi}{6} \times \frac{360}{2\pi} \]

### Step 4: Simplify the expression.
Now, we simplify the expression step by step:
1. Cancel \( \pi \) in the numerator and denominator:
\[ \text{Degrees} = \frac{7 \times 360}{6 \times 2} \]
2. Calculate \( 6 \times 2 = 12 \):
\[ \text{Degrees} = \frac{7 \times 360}{12} \]
3. Now, simplify \( \frac{360}{12} = 30 \):
\[ \text{Degrees} = 7 \times 30 \]
4. Finally, calculate \( 7 \times 30 = 210 \):
\[ \text{Degrees} = 210 \]

### Final Answer:
The degree measure of \( \frac{7\pi}{6} \) is \( 210 \) degrees.

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